A new approach for the fabrication of copper microgrooves with near triangular cross-sectional profile is introduced. For manufacturing the microgrooves, a laser-induced thermochemical etching technique based on an optical fiber as an optical waveguide and machining tool is proposed, which significantly reduced the complexity of a conventional laser etching set up. It is explained that the possible problem of fiber damage during laser etching with the proposed method can be solved by appropriately controlling the gap between the sample surface and fiber tip. The fabrication of copper microgrooves with $100{sim}300{mu}m$ in depth and $100{sim}150{mu}m$ in width is accomplished with the proposed technique. The grooves fabricated in the optimal process condition have smooth surfaces and clear edge. The angle of triangular groove is measured to be in the range of $30{sim}50$ degree and the aspect ratio of grooves is about $1{sim}2$. The overall etching results such as etch width, depth, and aspect ratio variation are reported in detail with respect to process variables.